Elastically Collective Nonlinear Langevin Equation Theory of Glass-Forming Liquids: Transient Localization, Thermodynamic Mapping, and Cooperativity

2018 ◽  
Vol 122 (35) ◽  
pp. 8451-8461 ◽  
Author(s):  
Anh D. Phan ◽  
Kenneth S. Schweizer
Keyword(s):  
Langevin Equation ◽  
Glass Forming ◽  
Nonlinear Langevin Equation

scholarly journals Coupling between structural relaxation and diffusion in glass-forming liquids under pressure variation

2020 ◽  
Vol 22 (42) ◽  
pp. 24365-24371
Author(s):  
Anh D. Phan ◽  
Kajetan Koperwas ◽  
Marian Paluch ◽  
Katsunori Wakabayashi
Keyword(s):  
Molecular Dynamics ◽  
Langevin Equation ◽  
Structural Relaxation ◽  
Md Simulations ◽  
Pressure Variation ◽  
Glass Forming ◽  
Nonlinear Langevin Equation ◽  
And Diffusion

We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulations.

scholarly journals On fractional Langevin equation involving two fractional orders in different intervals

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Hamid Baghani ◽  
J. Nieto
Keyword(s):  
Langevin Equation ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Numerical Examples ◽  
Fractional Equations ◽  
Fractional Langevin Equation ◽  
Nonlinear Langevin Equation ◽  
Fractional Orders

In this paper, we study a nonlinear Langevin equation involving two fractional orders  α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed. 

scholarly journals Effects of cooling rate on structural relaxation in amorphous drugs: elastically collective nonlinear langevin equation theory and machine learning study

RSC Advances ◽  
2019 ◽  
Vol 9 (69) ◽  
pp. 40214-40221 ◽  
Author(s):  
Anh D. Phan ◽  
Katsunori Wakabayashi ◽  
Marian Paluch ◽  
Vu D. Lam
Keyword(s):  
Machine Learning ◽  
Cooling Rate ◽  
Langevin Equation ◽  
Structural Relaxation ◽  
Molecular Mobility ◽  
Learning Study ◽  
Cooling Rates ◽  
Theoretical Approaches ◽  
Amorphous Drugs ◽  
Nonlinear Langevin Equation

Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs.

On a q-fractional variant of nonlinear Langevin equation of different orders

2014 ◽  
Vol 49 (6) ◽  
pp. 277-286 ◽  
Author(s):  
B. Ahmad ◽  
J. J. Nieto ◽  
A. Alsaedi ◽  
H. Al-Hutami
Keyword(s):  
Langevin Equation ◽  
Nonlinear Langevin Equation

scholarly journals Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Langevin Equation ◽  
Dirichlet Boundary ◽  
Contraction Mapping Principle ◽  
Dirichlet Boundary Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Single Index ◽  
New Type ◽  
Nonlinear Langevin Equation ◽  
Physical Phenomena ◽  
Fractional Orders

We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.

scholarly journals Nonlinear stochastic modelling with Langevin regression

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210092
Author(s):  
J. L. Callaham ◽  
J.-C. Loiseau ◽  
G. Rigas ◽  
S. L. Brunton
Keyword(s):  
Langevin Equation ◽  
Degrees Of Freedom ◽  
Bluff Body ◽  
Gaussian White Noise ◽  
Stochastic Modelling ◽  
State Dependent ◽  
Nonlinear Langevin Equation ◽  
Statistical Consistency ◽  
Fokker Planck Equations ◽  
Random Fluctuations

Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker–Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.

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